5x-7=3/2x=30

Solution for 5x-7=3/2x=30 equation:

5x-7=3/2x=30

We move all terms to the left:

5x-7-(3/2x)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

5x-(+3/2x)-7=0

We get rid of parentheses

5x-3/2x-7=0

We multiply all the terms by the denominator


5x*2x-7*2x-3=0

Wy multiply elements

10x^2-14x-3=0

a = 10; b = -14; c = -3;
Δ = b2-4ac
Δ = -142-4·10·(-3)
Δ = 316
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{316}=\sqrt{4*79}=\sqrt{4}*\sqrt{79}=2\sqrt{79}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{79}}{2*10}=\frac{14-2\sqrt{79}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{79}}{2*10}=\frac{14+2\sqrt{79}}{20}
$